In this paper, we give a numerical algorithm able to prove whether a set S described by nonlinear inequalities is path-connected or not. To our knowledge, no other algorithm (numerical or symbolic) is able to deal with this type of problem. The proposed approach uses interval arithmetic to build a graph which has exactly the same number of connected components as S. Examples illustrate the principle of the approach. © 2005 Elsevier B.V. All rights reserved.
Delanoue, N., Jaulin, L., & Cottenceau, B. (2006). Using interval arithmetic to prove that a set is path-connected. In Theoretical Computer Science (Vol. 351, pp. 119–128). https://doi.org/10.1016/j.tcs.2005.09.055